From heuristics to guarantees: the mathematical foundations of algorithms for data science

Many of the most successful approaches commonly used in data-science applications (e.g., machine learning) come with little or no guarantees. Notable examples include convolutional neural networks (CNNs) and data-fitting formulations based on non-convex loss functions. In both cases, the training procedures are based on optimizing over intractable problems. While these methods are undeniably successful in a wide variety of machine learning and signal-processing tasks (e.g., classification of images, speech, and text), the robustness that comes with theoretical guarantees are paramount for more critical applications such as in medical diagnoses or in unsupervised algorithms embedded into electronic devices (e.g., self-driving car). This project aims to build theoretical foundations for key algorithmic approaches used in data-science applications.